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Four prototypical flow fields are expressed below in terms of Cartesian coordinates. In these expressions, y is a constant. i) Planar elongation: ii) Uniaxial extension: iii) Biaxial extension: iv) Pure rotation: For each of these flows, determine: v=ixe - jye, +0e₂ v=2jxe - jy e, - ize, v = jxe + jy e, -2jze, v = iye - jxe, +0e₂ a) the rate of strain tensor € = ½ [Vy + Vy²] and b) the deviatoric stress tensor ( = ½ [Vy – Vy7]. - Based only on your answers to parts (a) and (b), determine: c) whether the flow is incompressible (i.e., is V. y = 0?) d) whether the flow is irrotational. (i.e., is V × v = 0 ?)

Four prototypical flow fields are expressed below in terms of Cartesian coordinates. In these expressions, y is a constant. i) Planar elongation: ii) Uniaxial extension: iii) Biaxial extension: iv) Pure rotation: For each of these flows, determine: v=ixe - jye, +0e₂ v=2jxe - jy e, - ize, v = jxe + jy e, -2jze, v = iye - jxe, +0e₂ a) the rate of strain tensor € = ½ [Vy + Vy²] and b) the deviatoric stress tensor ( = ½ [Vy – Vy7]. - Based only on your answers to parts (a) and (b), determine: c) whether the flow is incompressible (i.e., is V. y = 0?) d) whether the flow is irrotational. (i.e., is V × v = 0 ?)

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Four prototypical flow fields are expressed below in terms of Cartesian coordinates. In these expressions, y is a constant. i) Planar elongation: ii) Uniaxial extension: iii) Biaxial extension: iv) Pure rotation: For each of these flows, determine: v = jxex - ¡ye, +0e₂ v=2jxex - jy e, - ize₂ v = jxẹx + jy ẹ, - 2jze₂ v = jye - jxe, +0e₂ a) the rate of strain tensor = e [Vy + Vy¹] and 2 b) the deviatoric stress tensor = [Vy - Vy¹]. Based only on your answers to parts (a) and (b), determine: c) whether the flow is incompressible (i.e., is V. y = 0?) d) whether the flow is irrotational. (i.e., is V × v = 0 ?)
Transcribed Image Text:Four prototypical flow fields are expressed below in terms of Cartesian coordinates. In these expressions, y is a constant. i) Planar elongation: ii) Uniaxial extension: iii) Biaxial extension: iv) Pure rotation: For each of these flows, determine: v = jxex - ¡ye, +0e₂ v=2jxex - jy e, - ize₂ v = jxẹx + jy ẹ, - 2jze₂ v = jye - jxe, +0e₂ a) the rate of strain tensor = e [Vy + Vy¹] and 2 b) the deviatoric stress tensor = [Vy - Vy¹]. Based only on your answers to parts (a) and (b), determine: c) whether the flow is incompressible (i.e., is V. y = 0?) d) whether the flow is irrotational. (i.e., is V × v = 0 ?)
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